On the dynamics of imperfect shear deformable microplates

This paper investigates the nonlinear forced dynamical behaviour of a geometrically imperfect viscoelastic shear-deformable microplate. The third-order shear deformation plate theory and the Kelvin-Voigt viscoelastic model are utilised in the framework of the modified version of the couple-stress theory to develop a model for the microsystem. The developed model is in the form of partial differential equations (PDEs) and accounts for geometric nonlinearities, damping nonlinearities, micro-scale size effects, and initial imperfection. Five coupled PDEs are derived for the five independent displacements and rotations. These PDEs are truncated to a set of nonlinearly coupled ordinary differential equations via application of a two-dimensional modal decomposition based on the Galerkin technique. The final set of equations consists of quadratic and cubic nonlinear terms for both damping and stiffness. An efficient numerical algorithm based on a continuation scheme is utilised to analyse the nonlinear forced vibration characteristics of such complicated system. The effects imperfection amplitude, damping nonlinearities, and micro-scale size on forced resonant vibration response are highlighted.